Critical behaviour

Not only at lowtemperatures does the mean-field theory fail to account properly for the temperature dependence of the magnetization of a ferromagnet. There is a discrepancy in the critical region, close to T_C where the variation of M with temperature is as (T − T_C)^β with β ≈ 0.34, rather than 1/2. If the magnetization is calculated from molecular field theory using the measured exchange parameters (r_ij ) derived from spin-wave dispersion relations, the discrepancy in the predicted and measured values of T_C may be as great as 60%. This is partly due to spin waves, but the exchange parameters are renormalized to lower values on increasing temperature because of critical fluctuations. These remarkable fluctuations, which are self-similar over a wide range of length scales.

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